Eclipse is showing the following errors in my Spring's applicationContext.xml:

cvc-complex-type.2.4.c: The matching wildcard is strict, but no declaration can be found for element 'dwr:configuration'. myappservlet-servlet.xml MyApp/src/main/webapp/WEB-INF line 23 XML Problem
cvc-complex-type.2.4.c: The matching wildcard is strict, but no declaration can be found for element 'dwr:controller'. myappservlet-servlet.xml MyApp/src/main/webapp/WEB-INF line 21 XML Problem
cvc-complex-type.2.4.c: The matching wildcard is strict, but no declaration can be found for element 'dwr:remote'. myappservlet-servlet.xml MyApp/src/main/webapp/WEB-INF line 41 XML Problem

When I hover my mouse over the line-item error, it also says:

- schema_reference.4: Failed to read schema document 'http://www.directwebremoting.org/
schema/spring-dwr-3.0.xsd', because 1) could not find the document; 2) the document could not be
read; 3) the root element of the document is not <xsd:schema>.

I confirmed that the root element is in fact <xsd:schema>. When I use autocomplete by typing <dwr: Eclipse correctly shows me the various options like <dwr:configuration>, <dwr:controller>, etc. How can Eclipse know this without reading the schema?

I make use of many different namespaces without issue; the DWR schema is the only one that isn't being resolved. Here is the declaration:

I'm not sure what your question is here. You seem to answer it yourself in the last paragraph - DWR site goes down, schema validation in Eclipse fails. Note that Eclipse (even with the Spring IDE plugin) doesn't use META-INF/spring.schemas to resolve the namespaces, that's done by the Eclipse platform. If the schema can't be found at the schema location, then you get these errors.

As for the auto-complete, Eclipse will still provide this by inferring from existing structures in your document, if it can't find the schema.

This isn't a problem in the application itself, since Spring will use the META-INF/spring.schemas file to resolve schemas from the JAR.